How do I batch render the render layers that I have set up?
You were right the first time; all renderlayers are rendered when you press F12. You can view them independently in the image viewer:



Typically the compositor is used to combine renderlayers into a final image. 

To make the background transparent on one renderlayer and include the sky on another, you must use passes. 

Only settings located in the renderlayer panel can actually be set independently per-renderlayer, so enabling Film > Transparent will make the background transparent in all renderlayers. To get the background, there are two approaches, both using the Environment pass:


Create a separate renderlayer that doesn't render any objects, but with the Environment pass enabled. Then alpha over the desired renderlayers using the compositor:



This is the simpler of the two, but it requires the slight overhead of rendering the sky separately (you can set the samples to 1 on just the sky renderlayer to mitigate this)
Mix the environment passes of all the other renderlayers to get a all the background/sky you need to cover the areas not obscured by objects in both other renderlayers:



Potentially slightly faster, but you're not guaranteed to get the entire sky.




Note that there are a lot of different "layer" settings surrounding renderlayers, which can be rather confusing. See my answer here for more detail.

I've written this answer from the perspective of cycles. For BI it's a little different.